polynomiaalinen

Polynomiaalinen is Finnish adjective meaning related to polynomials or described by polynomials. It is used in mathematics, computer science, and numerical analysis to characterize expressions, functions, or growth that involve polynomials.

In mathematics polynomials are expressions formed from a finite sum of terms consisting of a coefficient and a non-negative integer power of a variable. A polynomial function is often written as p(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0, where a_n ≠ 0. The degree of the polynomial is n. Coefficients are typically taken from a field such as the real or complex numbers. Examples include linear polynomials like 2x + 3 and quadratic polynomials like x^2 − 5x + 6.

Key properties of polynomials include continuity and differentiability across their domain, and, over the complex numbers, the Fundamental Theorem of Algebra states that a non-constant polynomial has as many complex roots (counting multiplicities) as its degree. Real-coefficient polynomials factor into linear terms and irreducible quadratics, with complex roots occurring in conjugate pairs when coefficients are real.

In computer science and numerical analysis, polynomiaalinen growth describes time or space complexity that is a polynomial function of the input size, such as O(n^k) for some constant k. A polynomiaalinen algoritmi runs in polynomial time, which is contrasted with exponential or factorial growth. Related areas include polynomial interpolation, polynomial approximation, and methods for solving polynomial equations.